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2 years ago

HELP Plssss..... The m

Mathematics

1 answer:

hammer [34]2 years ago

6 0

Answer:

Step-by-step explanation:

Hey there!!!

According to the question,

Angle P is three less than twice less of an angle Q.

Then, let angle Q be x then angle P is 2x-3.

Now, it has also given that they are supplementary angle.

We know that the sum of supplementary angle is 180°.

Therefore, x+ 2x - 3°=180°.

Or, 3x = 180°-3°

Or, x = 177°/3

Therefore the measure of angle Q is 59° and P is 2×59°-3°= 121°.

Hope it helps....

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What is the nth term rule of the quadratic sequence below?

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Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

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As the first differences are not the same, calculate the second differences:

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

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The coefficient of the n² term is half of the second difference.

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Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences between the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

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